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76 Chapter 1: Limits and Their Properties
1.5 Infinite Limits
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine whether approaches or as x approaches from the
left and from the right by completing the tables below.
–3.1 –3.01 –3.001
–2.999 –2.99 –2.9 –2.5
a.
b.
c.
d.
____ 2. Find all the vertical asymptotes (if any) of the graph of the function
a.
b.
c.
d.
e. no vertical asymptotes
____ 3. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
1.5 Infinite Limits 77
____ 4. Find all the vertical asymptotes (if any) of the graph of the function
.
a.
b.
c.
d.
e.
____ 5. Find all the vertical asymptotes (if any) of the graph of the function .
a.
b.
c.
d.
e.
____ 6. Find all vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
____ 7. Find the vertical asymptotes (if any) of the function .
a.
b.
c.
d.
e.
____ 8. Find the limit.
a.
b.
c.
d.
e.
78 Chapter 1: Limits and Their Properties
____ 9. Find the limit.
a.
b.
c.
d.
e.
____ 10. Find the limit.
a.
b.
c.
d.
e.
____ 11. Find the limit (if it exists).
a.
b.
c.
d.
e.
____ 12. Use a graphing utility to graph the function and determine the
one-sided limit .
a.
b.
c. 0
d.
e. 8
1.5 Infinite Limits 79
____ 13. Use a graphing utility to graph the function and determine the
following one-sided limit.
a.
b.
c.
d.
e.
____ 14. A -foot ladder is leaning against a house (see figure). If the base of the ladder is
pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of
, where x is the distance between the base of the ladder and the house. Find the
rate r when x is feet.
a.
3
2
ft/sec
b.
4
3
ft/sec
c.
d.
2
3
ft/sec
e.
3
4
ft/sec
80 Chapter 1: Limits and Their Properties
____ 15. A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is
pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of
where x is the distance between the base of the ladder and the house. Find the
limit of r as .
a.
b.
c.
d.
e.
1.5 Infinite Limits 81
1.5 Infinite Limits
Answer Section
